so, 2 boxes, 1 contains a key, one a dagger
box1: “Either both inscriptions are true, or both are false.”
box2: “This box contains the key.”
The Jester’s logic was sound. To avoid paradox, the knife has to be in box2. If the knife is in box1, this is the analysis of the status of the inscriptions:
box2 is false for sure, since obviously the key was in box1
if box1 is true…well, essentially what box1 is saying is that the truth-value of both boxes has to be the same, so if box1 is true, and box2 is false, box1 must also be false, because it has to have the same truth-value as box 2. so “box1 is true” results in a contradiction.
if box1 is false on the other hand…well, that’s logically the same as saying that the truth value of the inscriptions are different. one is true and the other is false. but if both box1 and box2 are false, the “or both are false” part of the inscription on box1 is true, making box 1 true. So, box1 is false also results in a contradiction.
Both possible truth-values for box1 result in contradiction if the key is in box1…and yet it was. When I read that for the first time, it hit me really hard. The King’s response is absolutely brilliant: “I merely wrote those inscriptions on two boxes, and then I put the dagger in the second one.”
You can try it for yourself, as well. Take two envelopes and a ring, write on one envelope “Either both inscriptions are true or both are false,” put the ring in that envelope, and write on the other envelope “This envelope contains the ring.” You’ll find, I think, that reality doesn’t collapse in on itself. A black hole doesn’t suddenly form where the envelopes were. The world remains existent, you continue on living, pigs don’t fly, etc.
But something seems off, ya know? There’s a writing on an envelope, and what’s written on it is a truth statement. Normally, we’d think that a truth statement is either true or it’s false. But this thing is written, and it’s a truth statement, and if we assume it’s true…it’s false, and if we assume it’s false…it’s true! So what’s going on here? Right? Something weird is happening here. Logic’s getting turned on it’s head.
That’s what I thought until I realized that nothing actually contradictory had happened in the real world. You see, in our minds, we see a paradox, but in reality, the configuration of atoms that you arranged…are just a configuration of atoms. Nothing paradoxical happened. You made a series of pen strokes, and put a ring in an envelope. There’s nothing in there that implies that there is an actual logical paradox in reality. Despite our inability to evaluate the truth-value of the inscriptions on the box…well, just let what the king said sink in. “I merely wrote those inscriptions on two boxes, and then I put the dagger in the second one.”